Linear momentum conservation puzzle

[OceanBreeze]

In the problem under consideration, the system is isolated but it is not starting off at equilibrium. The unbalanced mass will shift from one battery to the other as it seeks equilibrium. For linear momentum and center of mass to be conserved, we are to assume that “something else” must provide for translational symmetry; finding that “something else” is the problem.

Hmmm, wait a second, I think everyone, including myself has been working with the assumption the mass shifts from the charged battery to the uncharged one, and stays there. That would require that something else shifts back the opposite direction to maintain center of mass and conservation of momentum.

But what if it doesn’t stay there? The initial condition we see is unbalanced and so not a stable condition. Once one battery discharges and transfers mass to the other, what is to prevent the other from doing the same thing? In a MGS, the motor and generator are basically the same thing, depending on where the input and output are taken.

So here is the scenario I see: The situation starts out with a charged battery and an uncharged battery, separated by the MGS. The charged battery will discharge into the motor and drive the generator, transferring charge to the other battery. The process will not stop when the charges are equalized because angular momentum keeps the rotor spinning past the equilibrium point. Now there is a charged battery on the generator side and a discharged battery on the motor side. So, the roles reverse and the motor and generator swap places. The system is an oscillator, with the charge going back and forth indefinitely. It won’t stop because of friction either because the system is completely isolated; there is nowhere for the heat to go!

The instantaneous center of mass shifts back and forth but the average center of mass is conserved, as is the average momentum.

 

[Q-reeus]

Hmmm, wait a second, I think everyone, including myself has been working with the assumption the mass shifts from the charged battery to the uncharged one, and stays there. That would require that something else shifts back the opposite direction to maintain center of mass and conservation of momentum.

But what if it doesn’t stay there? The initial condition we see is unbalanced and so not a stable condition. Once one battery discharges and transfers mass to the other, what is to prevent the other from doing the same thing? In a MGS, the motor and generator are basically the same thing, depending on where the input and output are taken.

So here is the scenario I see: The situation starts out with a charged battery and an uncharged battery, separated by the MGS. The charged battery will discharge into the motor and drive the generator, transferring charge to the other battery. The process will not stop when the charges are equalized because angular momentum keeps the rotor spinning past the equilibrium point. Now there is a charged battery on the generator side and a discharged battery on the motor side. So, the roles reverse and the motor and generator swap places. The system is an oscillator, with the charge going back and forth indefinitely. It won’t stop because of friction either because the system is completely isolated; there is nowhere for the heat to go!

The instantaneous center of mass shifts back and forth but the average center of mass is conserved, as is the average momentum.

Nice try but that won't do. If conservation of momentum is to hold as a fundamental principle, it must hold at every instant. The OP scenario only concerns itself with a one-way transfer of energy. That situation must be dealt with. Either the system COM remains constant at every instant, or not.

 

[OceanBreeze]

Nice try but that won't do. If conservation of momentum is to hold as a fundamental principle, it must hold at every instant. The OP scenario only concerns itself with a one-way transfer of energy. That situation must be dealt with. Either the system COM remains constant at every instant, or not.

I am not sure I agree. Here is my reasoning:
If the system is in SHM, (like a pendulum with a small amplitude) the center of mass stays put at the center of the system even though the pendulum mass swings back and forth.
However, the problem you posed had the system starting off in an unbalanced condition, like a pendulum with the weight held in one place. It would take an external force to hold the pendulum weight on one side, so the system is not isolated at that point. That is basically the way you have your MGS starting out. What you are doing is taking an instantaneous snapshot when the system is unbalanced and the com is not centered. I think that is what is causing the conundrum. We are looking for something that does not exist when the system oscillates.

 

[Q-reeus]

I am not sure I agree. Here is my reasoning:
If the system is in SHM, (like a pendulum with a small amplitude) the center of mass stays put at the center of the system even though the pendulum mass swings back and forth.
However, the problem you posed had the system starting off in an unbalanced condition, like a pendulum with the weight held in one place....

Depends what your definition of unbalanced is. The pendulum held to one side is in an unsymmetric configuration, but force and momentum balance continue to work just fine.

It would take an external force to hold the pendulum weight on one side, so the system is not isolated at that point.

Again, depends on your assumption there. If the catch is attached to the same frame holding the pendulum pivot, the system is isolated with a stationary COM. Which continues to hold if the catch is released without imparting an additional impulse by doing so.

That is basically the way you have your MGS starting out. What you are doing is taking an instantaneous snapshot when the system is unbalanced and the com is not centered. I think that is what is causing the conundrum. We are looking for something that does not exist when the system oscillates.

Nope. Whether on an instantaneous snapshot basis or final tally before vs after one, it's down to whether the system COM shifts, even transitively, or remains constant always.
Newton's 3rd Law demands the latter.

 

[OceanBreeze]

Depends what your definition of unbalanced is. The pendulum held to one side is in an unsymmetric configuration, but force and momentum balance continue to work just fine..

OK

Again, depends on your assumption there. If the catch is attached to the same frame holding the pendulum pivot, the system is isolated with a stationary COM. Which continues to hold if the catch is released without imparting an additional impulse by doing so..

OK, right. As the bob swings one way it exerts a force on the fulcrum and the fulcrum exerts a force on the frame moving the frame back the opposite way, maintaining com.

Nope. Whether on an instantaneous snapshot basis or final tally before vs after one, it's down to whether the system COM shifts, even transitively, or remains constant always.
Newton's 3rd Law demands the latter.

Ok. I do think the system will overshoot and oscillate, but you are right in that the com cannot move, not even in a transient way, so I was wrong about that.

Anyway, why can’t the magnetic field in the MGS act as the fulcrum, pushing the entire framework back as the battery mass swings to the other side? Is it because the fields only act purely torsional? Cannot the fields be shifted into a helical shape, with some translational component, or is that against the rules of the problem?

 

[Q-reeus]

Anyway, why can’t the magnetic field in the MGS act as the fulcrum, pushing the entire framework back as the battery mass swings to the other side? Is it because the fields only act purely torsional? Cannot the fields be shifted into a helical shape, with some translational component, or is that against the rules of the problem?

LOL. You are here getting to think like another poster The God who stares closely with a magnifying glass at every little minute of the arrangement. Hoping to find an overlooked electrical and/or magnetic circuit feature.

I guess it's time to give away one vital clue that should concentrate thinking. There is for sure an axial force acting within the shaft. It has the right direction and magnitude and temporal phase to exactly compensate for the electrochemical mass shift. Where does it come from - exactly? Thinking caps on. Back much later.

 

[hansda]

And? You do not accept that mass/energy in one battery has been exchanged with mass/energy in another such battery?

Lets name these two batteries as bat1 and bat2. Initially bat1 is charged and bat2 is discharged. Particle electron can not flow from bat1 to bat2 because these two batteries are electrically isolated. Particle photon can flow from bat1 to bat2. Particle photon carries energy and momentum but not mass. So, there is only energy and momentum transfer from bat1 to bat2. There is no mass transfer from bat1 to bat2.

There is no issue with an evident shift in COM to address?

As momentum shifts from bat1 to bat2; COM may shift in the direction bat2 to bat1.

 

[Q-reeus]

Lets name these two batteries as bat1 and bat2. Initially bat1 is charged and bat2 is discharged. Particle electron can not flow from bat1 to bat2 because these two batteries are electrically isolated. Particle photon can flow from bat1 to bat2. Particle photon carries energy and momentum but not mass. So, there is only energy and momentum transfer from bat1 to bat2. There is no mass transfer from bat1 to bat2.



As momentum shifts from bat1 to bat2; COM may shift in the direction bat2 to bat1.

Can't figure where you get photons flying between the two batteries. Nothing about e.g. some kind of laser beams system in OP. Gave the correct and vital clue in #66 hansda. I suggest concentrating on it.

 

[Fednis48]

I guess it's time to give away one vital clue that should concentrate thinking. There is for sure an axial force acting within the shaft. It has the right direction and magnitude and temporal phase to exactly compensate for the electrochemical mass shift. Where does it come from - exactly? Thinking caps on. Back much later.

For there to be an axial force, there has to be some kind of symmetry breaking. Thinking about variations on the setup and different battery designs, I can only point to one asymmetry that seems to always be present: there is a torsion gradient along the shaft, because the interactions with the two batteries are necessarily twisting it in opposite directions. I have no idea how this could lead to an axial force.

 

[Q-reeus]

For there to be an axial force, there has to be some kind of symmetry breaking. Thinking about variations on the setup and different battery designs, I can only point to one asymmetry that seems to always be present: there is a torsion gradient along the shaft, because the interactions with the two batteries are necessarily twisting it in opposite directions. I have no idea how this could lead to an axial force.

You are getting warm. Torsional gradient is an important factor. I'm amazed no-one has connected the dots by now, but then again, haven't seen a single reference to this problem mentioned in a textbook or online article, let alone solved. Despite the scenario being such an obvious one to tackle.

 

[hansda]

Can't figure where you get photons flying between the two batteries.

Magnetic fields are always associated with current. If current is transferred, magnetic fields will also be transferred. In essence EM energy or photon particles are transferred from bat1 to bat2.

Nothing about e.g. some kind of laser beams system in OP. Gave the correct and vital clue in #66 hansda. I suggest concentrating on it.

These photon particles carrying momentum, will travel through the shaft from bat1 to bat2. As a reaction the shaft will move from bat2 to bat1 direction.

 

[Q-reeus]

Magnetic fields are always associated with current.

Right, at least in classical setting, but....

If current is transferred, magnetic fields will also be transferred. In essence EM energy or photon particles are transferred from bat1 to bat2.

You don't seem to get the overall picture. At all. We need not have used batteries or even any electrical components. For instance, start with a spinning flywheel on one end of a shaft. A disk brake on the other end. Apply the brake. Energy transfers from one end to the other - via the spinning shaft. Start to get the essentials now?

These photon particles carrying momentum, will travel through the shaft from bat1 to bat2. As a reaction the shaft will move from bat2 to bat1 direction.

See above. The answer is intrinsic to within the shaft itself. No photons or magnetic fields or currents involved. Good thing for you folks I didn't place bets with any of you!

 

[OceanBreeze]

Right, at least in classical setting, but....

You don't seem to get the overall picture. At all. We need not have used batteries or even any electrical components. For instance, start with a spinning flywheel on one end of a shaft. A disk brake on the other end. Apply the brake. Energy transfers from one end to the other - via the spinning shaft. Start to get the essentials now?

See above. The answer is intrinsic to within the shaft itself. No photons or magnetic fields or currents involved. Good thing for you folks I didn't place bets with any of you!

So you are going to use the pseudovector associated with angular momentum, to conserve linear momentum?

I thought angular and linear momentum are separately conserved; that one does not convert into the other.
In other words, a change in angular momentum cannot result in a conservation of linear momentum.

 

[Q-reeus]

So you are going to use the pseudovector associated with angular momentum, to conserve linear momentum?

No. No connection at all.

I thought angular and linear momentum are separately conserved; that one does not convert into the other.

Correct. Which means above surmising is wrong.

In other words, a change in angular momentum cannot result in a conservation of linear momentum.

Redundant given the earlier line. No conversion or coupling per se.

 

[The God]

..... We need not have used batteries or even any electrical components. For instance, start with a spinning flywheel on one end of a shaft. A disk brake on the other end. Apply the brake. Energy transfers from one end to the other - via the spinning shaft. Start to get the essentials now?

See above. The answer is intrinsic to within the shaft itself. No photons or magnetic fields or currents involved. Good thing for you folks I didn't place bets with any of you!

Now stop fooling around, its more than 240 hrs as against asked 24 hrs.

 

[Q-reeus]

Now stop fooling around, its more than 240 hrs as against asked 24 hrs.

Can I take that as an admission you have run out of ideas?

 

[The God]

Can I take that as an admission you have run out of ideas?

No, you have chewed it to death, got yourself entangled, and finding it difficult to get out of it.

You changed the goal post from batteries MG set to fly wheel brake system. Now you will say that heat in the brakes will increase the KE and momentum of particles around, that will take care of KE, Momentum conservation as well as shifting of any COM.

You can make the similar claim in battery system as chemical reaction would lead to release of energy thus changing the surrounding T and things follow after that.

 

[Q-reeus]

No, you have chewed it to death, got yourself entangled, and finding it difficult to get out of it.

Sorry to inform you, The God, but the conceptual tangling is all yours. There is a neat solution - you just can't see it. Still hoping someone else here will finally twig. Now that three vital clues have been given.

You changed the goal post from batteries MG set to fly wheel brake system. Now you will say that heat in the brakes will increase the KE and momentum of particles around, that will take care of KE, Momentum conservation as well as shifting of any COM.

I haven't changed the goal posts at all. Maybe given them a fresh coat of paint.

You can make the similar claim in battery system as chemical reaction would lead to release of energy thus changing the surrounding T and things follow after that.

To repeat - answer has nothing to do with any such thermal etc. considerations. I specified an ideal process with 100% conversion efficiency. Flywheel-disk brake example is another variant, but environmental heating there has no bearing on the essential physics.

 

[hansda]

Right, at least in classical setting, but....

You don't seem to get the overall picture. At all. We need not have used batteries or even any electrical components. For instance, start with a spinning flywheel on one end of a shaft. A disk brake on the other end. Apply the brake. Energy transfers from one end to the other - via the spinning shaft. Start to get the essentials now?

See above. The answer is intrinsic to within the shaft itself. No photons or magnetic fields or currents involved. Good thing for you folks I didn't place bets with any of you!

May be my approach is different. What about my answer. Is it right or wrong?

 

[Q-reeus]

May be my approach is different. What about my answer. Is it right or wrong?

You mean the last part of your 2nd line in #71? This is not a guessing game hansda. What I expect - no, what I still hope for - is that someone will pick up the clues now out there, and join the dots.
Just to throw in an additional tantalizing tidbit; an axial impulse, which is there, is not a truly general resolution.
But before expanding on that, I want someone to see and point to exactly how an axial impulse in the shaft arises at all. And give a quantitative answer.
Back much later.